Formal Book

8 Some irrational numbers

Theorem 8.1

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$e$ is irrational

Proof ▶

Theorem 8.2

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$e^{2}$ is irrational

Proof ▶

Theorem 8.3 Little Lemma

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TODO

Proof ▶

Theorem 8.4

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$e^{4}$ is irrational

Proof ▶

Lemma 8.5

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TODO

Proof ▶

Lemma 8.6

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TODO

Proof ▶

Lemma 8.7

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TODO

Proof ▶

Theorem 8.8

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$e^{r}$ is irrational for every $r \in Q ∖ {0}$ .

Proof ▶

Theorem 8.9

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$π^{2}$ is irrational.

Proof ▶

Theorem 8.10

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For every odd integer $n \geq 3$ , the number

A (n) := \frac{1}{π} \arccos (\frac{1}{\sqrt{n}})

is irrational.

Proof ▶